Space-time block coding in orthogonal frequency division communication systems

ABSTRACT

Transmitters, receivers, and methods for providing improved transmit diversity orthogonal frequency division multiplexed communication systems is provided.

CROSS REFERENCE TO RELATED APPLICATIONS

This application claims priority from Provisional Application No.60/572,160, filed May 17, 2004, entitled “Space-Time Block Coding forOFDM via Time Domain Processing,” which is assigned to the assignee ofthe present application and fully incorporated herein by reference inits entirety.

BACKGROUND OF THE DISCLOSURE

The present disclosure relates to wireless communication systems, andmore particularly to transmission diversity in orthogonal frequencydivision multiplexing systems.

Demand for wireless digital communication and data processing systems ison the rise. Inherent in most digital communication channels are errorsintroduced when transferring frames, packets or cells containing dataover a channel that has some characteristics. Such errors are oftencaused by interference or thermal noise. The bit error rates of wirelesstransmission systems pose certain difficulties in designing encoding anddecoding schemes for data to be transmitted via such systems. Partlybecause of its mathematical tractability and partly because of itsapplication to a broad class of physical communication channels, theadditive white Gaussian noise (AWGN) model is often used to characterizethe noise in most communication channels.

One type of wireless communication system is an Orthogonal FrequencyDivision Multiplexed (OFDM) system. OFDM is a multi-carrier modulationtechnique that partitions the overall system bandwidth into multiple (N)orthogonal frequency subcarriers. These subcarriers may also be calledtones, bins, and frequency channels. Each subcarrier may be modulatedwith data. Up to N modulation symbols may be sent on the N totalsubcarriers in each OFDM symbol period. These modulation symbols areconverted to the time-domain with an N-point inverse fast Fouriertransform (IFFT) to generate a transformed symbol that contains Ntime-domain chips or samples.

To improve transmission diversity, space-time block coding in each ofthe two transmission paths has been developed, as described in Alamouti,“Space-Time Block Coding, A Simple Transmit Diversity Technique forWireless Communications”, IEEE Journal on Selected Areas inCommunications, Volume 16, pp. 1451-1458, October 1998, the content ofwhich is incorporated herein by reference in its entirety. The channelis assumed to be time/frequency invariant (flat) and is further assumedto remain constant over at least two consecutive symbols.

In accordance with the transmission scheme described in Alamouti, theoriginal symbol sequence x(n) is divided into blocks of two consecutivesymbols x_(k)(n) and x_(k+1)(n). In Alamouti every pair of symbols issubsequently mapped according to the following: $\begin{matrix}{ \begin{bmatrix}x_{k} \\x_{k + 1}\end{bmatrix}\Rightarrow\begin{bmatrix}x_{k} & {- x_{k + 1}} \\x_{k + 1}^{*} & x_{k}^{*}\end{bmatrix}  = \aleph} & (1.1)\end{matrix}$where for simplicity, time-index n is not included in expression (1.1)

Symbols x_(k) and x_(k+1)*, are transmitted at time k respectively fromthe first and second transmit antennas. Symbols −x_(k+1) and x_(k)* aretransmitted at time k+1 respectively from the first and second transmitantennas. The corresponding received signal r_(k), r_(k+1) at times kand k+1 are defined by the following expressions:r _(k) =x _(k) h ₁ +x _(k+1) *h ₂ +n _(k)r _(k+1) =−x _(k+1) h ₁ +x _(k) *h ₂ +n _(k+1)  (1.2)where h₁ and h₂ respectively represent the channels associated with thefirst and second transmission paths, and are further assumed to beconstant over two symbol periods. The received signals r_(k), r_(k+1)may be written as follows: $\begin{matrix}\begin{matrix}{{r_{k}{\bullet\begin{bmatrix}r_{k} \\r_{k + 1}^{*}\end{bmatrix}}} = {{\begin{bmatrix}h_{1} & {- h_{2}} \\h_{2}^{*} & h_{1}^{*}\end{bmatrix}\begin{bmatrix}x_{k} \\x_{k + 1}\end{bmatrix}} + \begin{bmatrix}n_{k} \\n_{k + 1}^{*}\end{bmatrix}}} \\{= {{H \cdot {\overset{\sim}{x}}_{k}} + {\overset{\sim}{n}}_{k}}}\end{matrix} & (1.3)\end{matrix}$

It is understood that the channel matrix H is orthogonal and that anoptimum receiver for this transmit diversity scheme multiplies r_(k) byH*, which is the matched filter receiver, to get two decision statisticsfor x_(k) and x_(k+1), i.e., to recover the transmitted symbols. Usingthis method, a diversity order of two is achieved at a receiver with asingle receive antenna.

The method described above may be adapted for use in OFDM systems byreplacing the time-domain computations with frequency-domaincomputations. Assume X_(n) and X_(n+1) are two OFDM symbols to betransmitted on sub-carriers n and n+1 in an OFDM system. In addition,for each transmit antenna m assume the channel remains constant over twoconsecutive sub-carriers. That isH_(m,n)≈H_(m,n+1)=H_(m)  (1.4)

By replacing the time-domain computations with frequency-domaincomputations, the received signal vector corresponding to sub-carriers nand n+1 may be written as: $\begin{matrix}{{R_{k}{\bullet\begin{bmatrix}R_{k} \\R_{k + 1}^{*}\end{bmatrix}}} = {{\begin{bmatrix}H_{1} & {- H_{2}} \\H_{2}^{*} & H_{1}^{*}\end{bmatrix}\begin{bmatrix}X_{k} \\X_{k + 1}^{*}\end{bmatrix}} + \begin{bmatrix}V_{k} \\V_{k + 1}^{*}\end{bmatrix}}} & (1.5)\end{matrix}$thus achieving a diversity of 2.

FIG. 1 is a block diagram of a portion of an OFDM transmitter 10described above. Each OFDM symbol of size N is divided into N/2 groupsof symbol pairs [X_(n) X_(n+1)]. Each such pair of symbols is thenencoded by the space-frequency encoder 12 to generate two differentpairs of symbols [X_(n)−X_(n+1)] and [X_(n+1)* X_(n)*]. Symbol pairs[X_(n)−X_(n+1)] are grouped into an N—symbol vector that is supplied toan inverse fast Fourier transform (IFFT) 18 block, which in response,generates an associated time-domain vector x₁ that is transmitted fromantenna 14. Similarly, symbol pairs [X_(n+1)*, X_(n)*] are grouped intoanother N—symbol vector that is supplied to IFFT 20 block, which inresponse, generates an associated time-domain vector x₂ that istransmitted from antenna 16.

As is seen from FIG. 1 and described above, the space-frequency encodingis performed on the input symbols, i.e., in the frequency domain.Accordingly, space-encoder 12 is required to generate two differentstreams and hence two separate IFFT blocks 18, 20, each associated witha different transmit antenna, are required for every transmitted OFDMsymbol.

BRIEF SUMMARY OF THE DISCLOSURE

In an embodiment, a transmitter comprises at least two antennas and aprocessor. The processor causes a reversed complex conjugate of a secondblock to be transmitted from a first antenna during a first time slotand a first block to be transmitted from the first antenna during asecond time slot after the first time slot, and causes the reversedcomplex conjugate of the first block to be transmitted from a secondantenna during the first time slot and the second block to betransmitted from the second antenna during the second time slot.

In another embodiment, a method comprises generating a first blockcomprises a first sequence, generating a second block comprising asecond sequence, forming a reversed complex conjugate of the firstblock, forming a reversed complex conjugate of the second block,providing the reversed complex conjugate of the second block followed bythe first block for transmission from a first antenna, and providing thereversed complex conjugate of the first block followed by the secondblock for transmission from a second antenna.

In a further embodiment, a method of generating blocks for transmissioncomprises generating a first block, generating a second block, forming acomplex conjugate of the second block, and providing the complexconjugate of the second block in an inverse of the first order followedby the first block for transmission from a first antenna.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 is a simplified high-level block diagram of some blocks of anOFDM transmitter, as known in the prior art.

FIG. 2 is a simplified high-level block diagram of a transmitter systemand a receiver system in a MIMO system in accordance with oneembodiment.

FIG. 3 is a simplified high-level block diagram of a transmitter inaccordance with one embodiment.

FIG. 4 shows symbols with respective cyclic prefixes for transmission inaccordance with one embodiment.

FIG. 5 is a simplified high-level block diagram of some blocks of anOFDM receiver, in accordance with one embodiment.

DETAILED DESCRIPTION OF THE DISCLOSURE

Referring to FIG. 2, a block diagram of an embodiment of a transmittersystem 110 and a receiver system 150 in a MIMO system 100 isillustrated. At transmitter system 110, traffic data for a number ofdata streams is provided from a data source 112 to a transmit (TX) dataprocessor 114. In an embodiment, each data stream is transmitted over arespective transmit antenna. TX data processor 114 formats, codes, andinterleaves the traffic data for each data stream based on a particularcoding scheme selected for that data stream to provide coded data.

The coded data for each data stream may be multiplexed with pilot datausing, for example, time division multiplexing (TDM) or code divisionmultiplexing (CDM). The pilot data is typically a known data patternthat is processed in a known manner (if at all), and may be used at thereceiver system to estimate the channel response. The multiplexed pilotand coded data for each data stream is then modulated (i.e., symbolmapped) based on a particular modulation scheme (e.g., BPSK, QSPK,M-PSK, or M-QAM) selected for that data stream to provide modulationsymbols. The data rate, coding, and modulation for each data stream maybe determined by controls provided by a processor 130.

The modulation symbols for all data streams are then provided to a TXMIMO processor 120, which may further process the modulation symbols(e.g., for OFDM). TX MIMO processor 120 then provides N_(T) modulationsymbol streams to N_(T) transmitters (TMTR) 122 a through 122 t. In anembodiment, TX MIMO processor 120 may provide the modulation symbols sothat transmission symbols are arragned to be transmitted in pairs, whereeach pair is transmitted from at least two antennas and with each symbolbeing a sequentially reversed complex conjugate version of a symbol thatis transmitted from another antenna as part of a same pair.

Each transmitter 122 receives and processes symbol pairs in the form ofsymbol streams and provides one or more analog signals, and furtherconditions (e.g., amplifies, filters, and upconverts) the analog signalsto provide a modulated signal suitable for transmission over the MIMOchannel. N_(T) modulated signals from transmitters 122 a through 122 tare then transmitted from N_(T) antennas 124 a through 124 t,respectively.

At receiver system 150, the transmitted modulated signals are receivedby N_(R) antennas 152 a through 152 r, and the received signal from eachantenna 152 is provided to a respective receiver (RCVR) 154. Eachreceiver 154 conditions (e.g., filters, amplifies, and downconverts) arespective received signal, digitizes the conditioned signal to providesamples, and further processes the samples to provide a corresponding“received” symbol stream.

An RX MIMO/data processor 160 then receives and processes the N_(R)received symbol streams from N_(R) receivers 154 based on a particularreceiver processing technique to provide N_(T) “detected” symbolstreams. The processing by RX MIMO/data processor 160 is described infurther detail below. Each detected symbol stream includes symbols thatare estimates of the modulation symbols transmitted for thecorresponding data stream. RX MIMO/data processor 160 then demodulates,deinterleaves, and decodes each detected symbol stream to recover thetraffic data for the data stream. The processing by RX MIMO/dataprocessor 160 is complementary to that performed by TX MIMO processor120 and TX data processor 114 at transmitter system 110.

RX MIMO processor 160 may derive an estimate of the channel responsebetween the N_(T) transmit and N_(R) receive antennas, e.g., based onthe pilot multiplexed with the traffic data. The channel responseestimate may be used to perform space or space/time processing at thereceiver. RX MIMO processor 160 may further estimate thesignal-to-noise-and-interference ratios (SNRs) of the detected symbolstreams, and possibly other channel characteristics, and provides thesequantities to a processor 170. RX MIMO/data processor 160 or processor170 may further derive an estimate of the “operating” SNR for thesystem, which is indicative of the conditions of the communication link.Processor 170 then provides channel state information (CSI), which maycomprise various types of information regarding the communication linkand/or the received data stream. For example, the CSI may comprise onlythe operating SNR. The CSI is then processed by a TX data processor 178,modulated by a modulator 180, conditioned by transmitters 154 a through154 r, and transmitted back to transmitter system 110.

At transmitter system 110, the modulated signals from receiver system150 are received by antennas 124, conditioned by receivers 122,demodulated by a demodulator 140, and processed by a RX data processor142 to recover the CSI reported by the receiver system. The reported CSIis then provided to processor 130 and used to (1) determine the datarates and coding and modulation schemes to be used for the data streamsand (2) generate various controls for TX data processor 114 and TX MIMOprocessor 120.

Processors 130 and 170 direct the operation at the transmitter andreceiver systems that they are coupled with including the appropriatetransmit and receive data processors. Memories 132 and 172 providestorage for program codes and data used by processors 130 and 170,respectively.

Referring to FIG. 3, a functional block diagram of a transmitter systemincluding multiple transmit antennas according to one embodiment isillustrated. In one embodiment, a separate data rate and coding andmodulation scheme may be used for each of the N_(T) data streams to betransmitted on the N_(T) transmit antennas (i.e., separate coding andmodulation on a per-antenna basis). The specific data rate and codingand modulation schemes to be used for each transmit antenna may bedetermined based on controls provided by processor a 130 (FIG. 1), andthe data rates may be determined as described above.

Transmitter unit 100 includes, in one embodiment, a transmit dataprocessor 202 that receives, codes, and modulates each data stream inaccordance with a separate coding and modulation scheme to providemodulation symbols and transmit MIMO Transmit data processor 202 andtransmit processor 204 are one embodiment of transmit data processor 114and transmit processor 120, respectively, of FIG. 1.

In one embodiment, as shown in FIG. 2, transmit data processor 202includes demultiplexer 210, N_(T) encoders 212 a through 212 t, andN_(T) channel interleavers 214 a through 214 t (i.e., one set ofdemultiplexers, encoders, and channel interleavers for each transmitantenna). Demultiplexer 210 demultiplexes data (i.e., the informationbits) into N_(T) data streams for the N_(T) transmit antennas to be usedfor data transmission. The N_(T) data streams may be associated withdifferent data rates, as determined by rate control functionality, whichin one embodiment may be provided by processor 130 or 170 (FIG. 1). Eachdata stream is provided to a respective encoder 212 a through 212 t.

Each encoder 212 a through 212 t receives and codes a respective datastream based on the specific coding scheme selected for that data streamto provide coded bits. In one embodiment, the coding may be used toincrease the reliability of data transmission. The coding scheme mayinclude in one embodiment any combination of cyclic redundancy check(CRC) coding, convolutional coding, Turbo coding, block coding, or thelike. The coded bits from each encoder 212 a through 212 t are thenprovided to a respective channel interleaver 214 a through 214 t, whichinterleaves the coded bits based on a particular interleaving scheme.The interleaving provides time diversity for the coded bits, permits thedata to be transmitted based on an average SNR for the transmissionchannels used for the data stream, combats fading, and further removescorrelation between coded bits used to form each modulation symbol.

The coded and interleaved bits from each channel interleaver 214 athrough 214 t are provided to a respective symbol mapping block 222 athrough 222 t, of transmit processor 204, which maps these bits to formmodulation symbols.

The particular modulation scheme to be implemented by each symbolmapping block 222 a through 222 t is determined by the modulationcontrol provided by processor 130 (FIG. 1). Each symbol mapping block222 a through 222 t groups sets of q_(j) coded and interleaved bits toform non-binary symbols, and further maps each non-binary symbol to aspecific point in a signal constellation corresponding to the selectedmodulation scheme (e.g., QPSK, M-PSK, M-QAM, or some other modulationscheme). Each mapped signal point corresponds to an M_(j)-ary modulationsymbol, where M_(j) corresponds to the specific modulation schemeselected for the j-th transmit antenna and M_(j)=2^(q) ^(j) . Symbolmapping blocks 422 a through 222 t then provide N_(T) streams ofmodulation symbols.

In the specific embodiment illustrated in FIG. 3, transmit processor 304also includes a modulator 224 and inverse Fast Fourier transform (IFFT)block 226 a through 226 t, along with symbol mapping blocks 222 athrough 222 t. Modulator 224 modulates the samples to form themodulation symbols for the N_(T) streams on the proper subbands andtransmit antennas. In addition modulator 224 provides each of the N_(T)symbol streams at a proscribed power level. In one embodiment, modulator224 may modulate symbols according to a FH sequence controlled by aprocessor, e.g. processor 130 or 170. In such an embodiment, thefrequencies with which the N_(T) symbol streams are modulated may varyfor each group or block of symbols, frame, or portion of a frame of atransmission cycle.

Each IFFT block 226 a through 226 t receives a respective modulationsymbol stream from modulator 224. Each IFFT block 226 a through 226 tgroups sets of NF modulation symbols to form corresponding modulationsymbol vectors, and converts each modulation symbol vector into itstime-domain representation (which is referred to as an OFDM symbol)using the inverse fast Fourier transform. IFFT blocks 226 a through 226t may be designed to perform the inverse transform on any number offrequency subchannels (e.g., 8, 16, 32, . . . , N_(F),). Eachtime-domain representation of the modulation symbol vector generated byIFFT blocks 226 a through 226 t is provided to encoder 228.

In the embodiment of FIG. 2, modulated data includes symbols which mayprovided in a symbol stream, e.g. symbols X_(i), X_(i+1), . . . X_(n).IFFT blocks 226 a through 226 t receive the symbol stream, symbolsX_(i), X_(i+1), . . . X_(n) and provide time domain sequences of eachsymbol that correspond to the samples of each symbol, e.g. sequencex_(i) for symbol X_(i), sequence x_(i+1) for symbol X_(i+1), andsequence x_(n) for symbol X_(n). Encoder 228, using the receivedsequences x_(i), x_(i+1), . . . x_(n) generates sequences {tilde over(x)}_(i), −{tilde over (x)}_(i+1), . . . −{tilde over (x)}_(N) Wheresequence {tilde over (x)}_(i) is a reversed complex conjugate sequenceof sequence x_(i), sequence {tilde over (x)}_(i+1) is a reversed complexconjugate sequence associated with sequence x_(i+1), etc. Encoder 228provides symbol pairs to transmitters 230 a through 232 t, so that anysymbol pair that is transmitted from two or more antennas is transmittedin the form of −{tilde over (x)}_(i+1), x_(i) from a first antenna, e.g.antenna 232 a, in first and second time slots and is transmitted in theform of {tilde over (x)}_(i), x_(i+1) from a second antenna, e.g.antenna 232 b, in the first and second time slots. In other words,during time slot i, sequence −{tilde over (x)}_(i+1) is transmitted fromtransmit antenna 232 a and sequence {tilde over (x)}_(i) is transmittedfrom transmit antenna 232 b. At time slot i+1, sequence {tilde over(x)}_(i) is transmitted from transmit antenna 232 a and sequence x_(i+1)is transmitted from transmit antenna 232 a.

For a symbol stream or group of symbols X_(i)(n)=X_(i)(n), n=0, 1, . . ., N−1, is the n-th information symbol in the i-th OFDM symbol. Thesequence for the i-th OFDM symbol may be defined, in vector format, asX _(i) =[X _(i)(0)X _(i)(1) . . . X _(i)(N−1)]^(T)  (2.1)

Let x_(i)(k), k=0, 1, . . . , N−1 represent the corresponding IFFToutput (i.e. the time domain samples of the symbol X_(i)), and let thesymbol energy E_(s)=E{X_(i)(n)X_(i)*(n)} be 1, i.e. the maximum energyallotted for transmission of the symbol. Further, let sequences x_(i)and x_(i+1) represent corresponding IFFT of consecutive OFDM symbolsX_(i) and X_(i+1). Using {tilde over (x)}_(i) and x_(i+1), sequences{tilde over (x)}_(i) and −{tilde over (x)}_(i+1) are defined as below:{tilde over (x)} _(i)(k)={overscore (x)} _(i)(N−K) 0≦k≦N−1{tilde over (x)} _(i+1)(k)={overscore (x)} _(i+1)(N−K) 0≦k≦N−1  (2.2)where {overscore ((•))} denotes a complex conjugate operation forscalars and element by element complex conjugate for vectors andmatrices. Accordingly, {tilde over (x)}_(i) and −{tilde over (x)}_(i+1)are ordinally reversed and element by element complex conjugatedsequences of x_(i) and x_(i+1), respectively.

The output of encoder 228 is coupled to cyclic prefix generators 230 athrough 230 t. The cyclic prefix generators 230 a through 230 tpre-pending a prefix of a fixed number of samples, which are generally anumber of samples from the end of the OFDM symbol, to the N_(S) samplesthat constitute an OFDM symbol to form a corresponding transmissionsymbol. The prefix is designed to improve performance againstdeleterious path effects such as channel dispersion caused by frequencyselective fading.

The symbols output by cyclic prefix generators 230 a through 230 t areprovided to an associated transmitter 232 a through 232 t which causesthe symbols to be transmitted by antennas 234 a through 234 t.

It should be noted that while the above discussion refers to X_(i) andX_(i+1) as symbols and x_(i) and x_(i+1) as time domain sequences ofsymbols X_(i) and X_(i+1), that the same approach may be applied toblocks of symbols or sequences. For example, X_(i) and X_(i+1) may eachrepresent N symbols, where N may greater than or less than 1. In such acase, x_(i) and x_(i+1) would represent time-domain sequences of Nsymbols and {tilde over (x)}_(i) and {tilde over (x)}_(i+1) are reversedcomplex conjugates of N symbols.

While the above discussion relates to an embodiment utilizing twosymbols transmitted over two time-slots, a greater number of symbolsover a larger number of time slots may also be utilized in accordancewith the embodiments described herein. In such embodiments, the matrix,which is defined by the number of transmission symbols and the number ofantennas, is a unitary matrix. This allows for different rates to beutilized for transmission, i.e. n transmit symbols per m transmitantennas where n>m. For example, a three antenna system consisting ofantennas a₁, a₂, and a₃ may transmit symbols x₁, x₂, x₃, and x₄ mayutilize the following transmission scheme which is defined by an x by amatrix M_(t) $\begin{pmatrix}x_{1} & x_{2} & x_{3} \\{- x_{2}} & x_{1} & {- x_{4}} \\{- x_{3}} & x_{4} & x_{1} \\{- x_{4}} & {- x_{3}} & x_{2} \\{\overset{\sim}{x}}_{1} & {\overset{\sim}{x}}_{2} & {\overset{\sim}{x}}_{3} \\{- {\overset{\sim}{x}}_{2}} & {\overset{\sim}{x}}_{1} & {- {\overset{\sim}{x}}_{4}} \\{- {\overset{\sim}{x}}_{3}} & {\overset{\sim}{x}}_{4} & {\overset{\sim}{x}}_{1} \\{- {\overset{\sim}{x}}_{4}} & {- {\overset{\sim}{x}}_{3}} & {\overset{\sim}{x}}_{2}\end{pmatrix}\quad M_{t}$where {tilde over (x)}₁, {tilde over (x)}₂, {tilde over (x)}₃, and{tilde over (x)}₄ are time reversed complex conjugates of symbols x₁,x₂, x₃, and x₄, respectively, −x₂, −x₃, and −X₄ are inverted symbols x₂,x₃, and x₄, respectively, and −{tilde over (x)}₂, −{tilde over (x)}₃,and −{tilde over (x)}₄ are inverted complex conjugates of symbols x₂,x₃, and x₄, respectively.The order of the symbols may be provided by encoder 228 in the orderspecified in M_(t) or any other scheme based upon a unitary matrix.In some embodiments, encoder 228 may comprise a memory, e.g. one or morebuffers, that stores the time domain symbols, their complex conjugates,their inverses, and inverted complex conjugates, and then may outputthem based upon a scheme based upon a unitary matrix to a plurality oftransmit antennas.

Referring to FIG. 4, symbols with respective cyclic prefixes fortransmission in accordance with one embodiment are illustrated. At timeslot i, time-domain sequence x_(i) is appended with its cyclic prefixand transmitted from a first transmit antenna, and time-domain sequence−{tilde over (x)}_(i+1) is appended with its cyclic prefix andtransmitted from a second transmit antenna. At time slot i+1,time-domain sequence x_(i+1) is appended with its cyclic prefix andtransmitted from the fist transmit antenna, and time-domain sequence{tilde over (x)}x_(i) is appended with its cyclic prefix and transmittedfrom the second transmit antenna.

Referring to FIG. 5, a simplified high-level block diagram of someblocks of an OFDM receiver, in accordance with one embodiment isillustrated. Receiver 400 is adapted to receive sequences y_(i) andy_(i+1) via receive antenna 402 and to demodulate and decode thesequences. As seen from FIG. 5, receiver 400 is shown as including, inpart, a discrete Fourier transform block 404, processing blocks 406 and408, each of which provides a complex conjugate function of the functionthe block receives, decoder/equalizer block 410, and block 412 whichperforms time reverse operation.

In transmission of the symbols or blocks, h_(m)(k) represents the symbolspaced channel impulse response for two transmit antennas m, m=1,2,where the first transmit antenna is represented by m=1 and the secondtransmit antenna is represented by m=2. In this case, h_(m)(k) may bedefined as: $\begin{matrix}{{h_{m}(k)} = {\sum\limits_{l = 0}^{L}{h_{m,l}{\delta( {k - l} )}}}} & (2.3)\end{matrix}$

At the receiver of the blocks or symbols, sequences y_(i) and y_(i+1)represent the received time-domain sequences corresponding to time slotsi and i+1, respectively, that are transmitted sequences x_(i) andx_(i+1) with their respective cyclic prefixes removed.

Sequences y_(i) and y_(i+1) received by receive antenna 402 are shownbelow:y _(i) =[y _(i)(0)y _(i)(1) . . . y _(i)(N−1)]^(T)y _(i+1) =[y _(i+1)(0)y _(i+1)(1) . . . y _(i+1)(N−1)]^(T)  (2.4)and may be expressed as shown below:y _(i) =H ₁ ·x _(i) −H ₂ ·{tilde over (x)} _(i+1) +v _(i)y _(i+1) =H ₁ ·x _(i+1) +H ₂ ·{tilde over (x)} _(i) +v _(i+1)  (2.5)where both sequences v_(i) and v_(i+1) are white independent identicallydistributed (i.i.d.) Gaussian random noise vectors with covariance σ²×I.Accordingly, the signal to noise ratio SNR is: $\begin{matrix}{{SNR} = {\rho = \frac{1}{\sigma^{2}}}} & (2.6)\end{matrix}$where H_(m),m=1,2 is the channel matrix corresponding to transmitantenna m and is given by: $\begin{matrix}{H_{m} = \begin{bmatrix}h_{m,0} & h_{m,1} & \cdots & h_{m,L} & 0 & \cdots & 0 \\0 & h_{m,0} & ⋰ & h_{m,{L - 1}} & h_{m,L} & \cdots & 0 \\0 & ⋰ & ⋰ & ⋰ & ⋰ & ⋰ & 0 \\0 & \cdots & 0 & h_{m,0} & h_{m,1} & \cdots & h_{m,L} \\h_{L} & 0 & \cdots & \cdots & h_{o} & \cdots & h_{L - 1} \\\vdots & ⋰ & ⋰ & ⋰ & ⋰ & ⋰ & \vdots \\h_{m,1} & \cdots & h_{m,L} & 0 & \cdots & 0 & h_{m,0}\end{bmatrix}} & (2.7)\end{matrix}$

The matrix H_(m) is circulant and has the following eigenvaluedecomposition:H _(m) =Q′Λ _(m) Q  (2.8)where Q is the N×N discrete Fourier transform matrix (DFT) as shownbelow: $\begin{matrix}{{Q( {k,n} )} = {\frac{1}{\sqrt{N}} \cdot {\mathbb{e}}^{{- j}\quad 2\pi\quad{{kn}/N}}}} & (2.9)\end{matrix}$and Λ_(m) is the diagonal eigenvalue matrix whose diagonal is the Npoint DFT of h_(m,0),h_(m,1), . . . ,h_(m,L).

Using the DFT property thatDFT({tilde over (x)} _(i))=DFT({overscore (x)} _(i) [−n]_(N))={overscore (X)}_(i)where by definition:X _(i) =DFT(x _(i))=Q·x _(i)V _(i) =DFT(v _(i))=Q·v _(i)the following expression (2.7) is attained. FFT block 402 receivessymbol (signal vector) y_(i) and, in response, generates signal vectorY_(i). FFT block 402 also receives signal vector y_(i+1) and, inresponse, generates signal vector Y_(i+1). Signal vectors Y_(i) andY_(i+1) are expressed as shown below: $\begin{matrix}{{Y_{i}\bullet\quad{Q \cdot y_{i}}} = {{{Q \cdot Q^{*}}\Lambda_{1}{Q \cdot x_{i}}} - {{Q \cdot Q^{*}}\Lambda_{2}{Q \cdot {\overset{\sim}{x}}_{i + 1}}} + {Q \cdot v_{i}}}} & (2.10) \\{\quad{= {{\Lambda_{1}X_{i}} - {\Lambda_{2}{\overset{\_}{X}}_{i + 1}} + V_{i}}}} & \quad \\{{Y_{i + 1}\bullet\quad{Q \cdot y_{i + 1}}} = {{{Q \cdot Q^{*}}\Lambda_{1}{Q \cdot x_{i + 1}}} + {{Q \cdot Q^{*}}\Lambda_{2}{Q \cdot {\overset{\sim}{x}}_{i}}} + {Q \cdot v_{i + 1}}}} & \quad \\{\quad{= {{\Lambda_{1}X_{i + 1}} - {\Lambda_{2}{\overset{\_}{X}}_{i}} + V_{i + 1}}}} & \quad\end{matrix}$

Signal vector Y_(i) is delivered to decoder/equalizer block 410. SignalY_(i+1) is delivered to processing block 104, which in response,generates and delivers to decoder/equalizer block 410, complex conjugatevector signal {overscore (Y)}_(i+1).

Expression (2.10) may be written as: $\begin{matrix}\begin{matrix}{Y_{i} = \begin{bmatrix}Y_{i} \\{\overset{\_}{Y}}_{i + 1}\end{bmatrix}} \\{= {{\begin{bmatrix}\Lambda_{1} & {- \Lambda_{2}} \\\Lambda_{2}^{*} & \Lambda_{1}^{*}\end{bmatrix}\begin{bmatrix}X_{i} \\{\overset{\_}{X}}_{i + 1}\end{bmatrix}} + \begin{bmatrix}V_{i} \\{\overset{\_}{V}}_{i + 1}\end{bmatrix}}} \\{= {{H \cdot X_{i}} + V_{i}}}\end{matrix} & (2.11)\end{matrix}$where Y_(i) is a 2N×1 vector. Since the DFT matrix Q is an orthogonalmatrix, the noise vector V_(i) is also white. Hence decoder/equalizerblock 410, which is adapted to perform a minimum mean-squared error(MMSE) as well as decoding/equalizing filter operation, is characterizedby the following matrix filter W: $\begin{matrix}{W = {\lbrack {{H \cdot H^{*}} + {\frac{1}{\rho} \cdot I}} \rbrack^{- 1}H}} & (2.12)\end{matrix}$

Assume that the channel impulse response associated with the first andsecond transmission channels is respectively represented by Λ₁ and Λ₂.Matrix D is defined as follows:D=Λ _(I)Λ₁*+Λ₂Λ₂*Matrix D is an N×N diagonal matrix whose (n,n) element d_(nn) is shownbelow:|Λ₁(i,i)|²+|Λ₂(i,i)|²Matrix {tilde over (D)} is defined as:$\overset{\sim}{D} = {D + {\frac{1}{\rho}I}}$where ρ is the SNR. Accordingly:{tilde over (D)} ⁻¹Λ_(m)=Λ_(m) {tilde over (D)} ⁻¹ and {tilde over (D)}⁻¹Λ_(m)*=Λ_(m) *{tilde over (D)} ⁻¹.Therefore, matrix W may be defined as shown below: $\begin{matrix}\begin{matrix}{W = {\begin{bmatrix}\Lambda_{1} & {- \Lambda_{2}} \\\Lambda_{2}^{*} & \Lambda_{1}^{*}\end{bmatrix}\begin{bmatrix}{\overset{\sim}{D}}^{- 1} & 0 \\0 & {\overset{\sim}{D}}^{- 1}\end{bmatrix}}} \\{= {W_{d} \cdot W_{e}}}\end{matrix} & (2.13)\end{matrix}$

As seen from expression (2.13), the matrix filter W includes two parts.The first part, W_(d), represents the decoding operation of thespace-time block code. The second part, W_(e), represents the MMSEfrequency domain equalizer part. Applying matrix filter W to thereceived signal vector Y_(i) provides the following: $\begin{matrix}\begin{matrix}{{\begin{bmatrix}Z_{i} \\Z_{i + 1}\end{bmatrix}\bullet\quad W{\overset{*}{y} \cdot Y_{i}}} = {{\overset{\sim}{D}}^{- 1} \cdot \begin{bmatrix}{{\Lambda_{1}^{*}Y_{i}} + {\Lambda_{2}{\overset{\_}{Y}}_{i + 1}}} \\{{{- \Lambda_{2}^{*}}Y_{i}} + {\Lambda_{1}{\overset{\_}{Y}}_{i + 1}}}\end{bmatrix}}} \\{= {{{\overset{\sim}{D}}^{- 1}{D \cdot \begin{bmatrix}X_{i} \\{\overset{\_}{X}}_{i + 1}\end{bmatrix}}} + \begin{bmatrix}{\overset{\sim}{V}}_{i} \\{\overset{\sim}{V}}_{i + 1}\end{bmatrix}}}\end{matrix} & (2.14)\end{matrix}$

Vectors Z_(i) and Z_(i+1) are generated by decoder/equalizer block 410.Expression (2.14) may be rewritten as shown below: $\begin{matrix}{\begin{bmatrix}Z_{i} \\{\overset{\_}{Z}}_{i + 1}\end{bmatrix} = {{{\overset{\sim}{D}}^{- 1}{D \cdot \begin{bmatrix}X_{i} \\X_{i + 1}\end{bmatrix}}} + \begin{bmatrix}{\overset{\sim}{V}}_{i} \\{\overset{\overset{\_}{\sim}}{V}}_{i + 1}\end{bmatrix}}} & (2.15)\end{matrix}$It is thus seen that matrix {tilde over (D)}⁻¹D is a diagonal matrixwhose (n,n) element g_(nn) is shown below: $\begin{matrix}{g_{nn} = \frac{{{\Lambda_{1}( {n,n} )}}^{2} + {{\Lambda_{2}( {n,n} )}}^{2}}{{{\Lambda_{1}( {n,n} )}}^{2} + {{\Lambda_{2}( {n,n} )}}^{2} + {1/\rho}}} & (2.16)\end{matrix}$It is also seen that the following expression applies:E{{tilde over (V)} _(i) {tilde over (V)} _(i) *}=E{{tilde over({overscore (V)})} _(i+1) {tilde over ({overscore (V)})} _(i+1) *}=R_(v)where R_(v) is an (n,n) diagonal matrix (n,n), whose element ξ_(nn) isprovided by the following expression: $\begin{matrix}{\zeta_{nn} = {\frac{1}{\rho} \cdot \frac{{{\Lambda_{1}( {n,n} )}}^{2} + {{\Lambda_{2}( {n,n} )}}^{2}}{( {{{\Lambda_{1}( {n,n} )}}^{2} + {{\Lambda_{2}( {n,n} )}}^{2} + {1/\rho}} )^{2}}}} & (2.17)\end{matrix}$where both {tilde over (V)}_(i) and {tilde over ({overscore (V)})}_(i+1)are independent identically distributed (i.i.d.) Gaussian randomvectors.

Using expressions (2.15), (2.16), and (2.17), the decision statistic{circumflex over (X)}_(i)(n) for symbol X_(i)(n), which is the n-thinformation symbol transmitted in the i-th OFDM block, may be expressedas shown below:s _(i)(n)=g _(nn) ·X _(i)(n)+v _(i)(n)  (2.18)and the corresponding signal-to-noise ratio (SNR) SNR_(i)(n) may beexpressed as shown below: $\begin{matrix}\begin{matrix}{{{SNR}_{i}(n)} = \frac{g_{nn}^{2}}{\zeta_{nn}}} \\{= {\rho \cdot ( {{{\Lambda_{1}( {n,n} )}}^{2} + {{\Lambda_{2}( {n,n} )}}^{2}} )}} \\{= {{SNR} \cdot ( {{{\Lambda_{1}( {n,n} )}}^{2} + {{\Lambda_{2}( {n,n} )}}^{2}} )}}\end{matrix} & (2.19)\end{matrix}$

Similarly, the decision statistic {circumflex over (X)}_(i+1)(n) forsymbol X_(i+1)(n), which is the n-th information symbol transmitted inthe i+1 OFDM block, may be expressed as shown below:s _(i+1)(n)=g _(nn) ·X _(i+1)(n)+v _(i+1)(n)  (2.20)and the corresponding signal to noise ration SNR_(i+1)(n) may beexpressed as shown below: $\begin{matrix}\begin{matrix}{{{SNR}_{i + 1}(n)} = \frac{g_{nn}^{2}}{\zeta_{nn}}} \\{= {\rho \cdot ( {{{\Lambda_{1}( {n,n} )}}^{2} + {{\Lambda_{2}( {n,n} )}}^{2}} )}} \\{= {{SNR} \cdot ( {{{\Lambda_{1}( {n,n} )}}^{2} + {{\Lambda_{2}( {n,n} )}}^{2}} )}}\end{matrix} & (2.21)\end{matrix}$Thus a diversity gain of order 2 is achieved.

In those cases, where more than two transmit antennas are utilized andmore than two transmit symbols are grouped together, receiver includesadditional outputs from decoder/equalizer block 410 which each providethe appropriate inversion and complex conjugation functions based uponthe number of transmit antennas at the transmitter.

The functionality described with respect to FIG. 5 may be implemented inreceive processor 142 and processor 130 and receive processor 160 andprocessor 170. In such a case, the functionality described with respectto elements 404, 406, 408, 410, and 412 may provided in the processors.

Those skilled in the art will appreciate that the various illustrativelogical blocks, modules, circuits, and algorithms described inconnection with the embodiments disclosed herein may be implemented aselectronic hardware, computer software, or combinations of both. Toclearly illustrate this interchangeability of hardware and software,various illustrative components, blocks, modules, circuits, andalgorithms have been described above generally in terms of theirfunctionality. Whether such functionality is implemented as hardware orsoftware depends upon the particular application and design constraintsimposed on the overall system. Skilled artisans may implement thedescribed functionality in varying ways for each particular application,but such implementation decisions should not be interpreted as causing adeparture from the scope of the present invention.

The various illustrative logical blocks, processors, modules, andcircuits described in connection with the embodiments disclosed hereinmay be implemented or performed with a general purpose processor, adigital signal processor (DSP), circuits, an application specificintegrated circuit (ASIC), a field programmable gate array (FPGA) orother programmable logic device, discrete gate or transistor logic,discrete hardware components, or any combination thereof designed toperform the functions described herein. A general purpose processor maybe a microprocessor, but in the alternative, the processor may be anyconventional processor, processor, microprocessor, or state machine. Aprocessor may also be implemented as a combination of devices, e.g., acombination of a DSP and a microprocessor, a plurality ofmicroprocessors, one or more microprocessors in conjunction with a DSPcore, multiple logic elements, multiple circuits, or any other suchconfiguration.

The methods or algorithms described in connection with the embodimentsdisclosed herein may be embodied directly in hardware, in a softwaremodule executed by a processor, or in a combination of the two. Asoftware module may reside in RAM memory, flash memory, ROM memory,EPROM memory, EEPROM memory, registers, hard disk, a removable disk, aCD-ROM, or any other form of storage medium known in the art. Anexemplary storage medium is coupled to the processor such the processorcan read information from, and write information to, the storage medium.In the alternative, the storage medium may be integral to the processor.The processor and the storage medium may reside in an ASIC. The ASIC mayreside in a user terminal. In the alternative, the processor and thestorage medium may reside as discrete components in a user terminal.

The previous description of the disclosed embodiments is provided toenable any person skilled in the art to make or use the presentinvention. Various modifications to these embodiments will be readilyapparent to those skilled in the art, and the generic principles definedherein may be applied to other embodiments without departing from thespirit or scope of the invention. Thus, the present invention is notintended to be limited to the embodiments shown herein but is to beaccorded the widest scope consistent with the principles and novelfeatures disclosed herein.

1. A transmitter comprising: at least two antennas; and a processorutilizing an inverse fast Fourier transform to generate a reversedcomplex conjugate of a first block and a second block, and causes thereversed complex conjugate of the second block to be transmitted from afirst antenna of the at least two antennas during a first time slot andthe first block to be transmitted from the first antenna during a secondtime slot after the first time slot, and causes the reversed complexconjugate of the first block to be transmitted from a second antenna ofthe at least two antennas during the first time slot and the secondblock to be transmitted from the second antenna during the second timeslot.
 2. The transmitter of claim 1, wherein the first time slot and thesecond time slot are consecutive time slots.
 3. The transmitter of claim1, wherein the first block consists of a first symbol and the secondblock consists of a second symbol.
 4. The transmitter of claim 3,wherein the first symbol and the second symbol are consecutive symbolsof a symbol stream.
 5. The transmitter of claim 4, wherein the firstsymbol and the second symbol are non-consecutive symbols of a symbolstream.
 6. The transmitter of claim 4, further comprising a memory thatstores the first block, second block, reversed complex conjugate of thefirst block, and reversed complex conjugate of the second block, andthat outputs the reversed complex conjugate of the second block to betransmitted from the first antenna of the at least two antennas duringthe first time slot, the first block to be transmitted from the firstantenna during the second time slot after the first time slot, thereversed complex conjugate of the first block to be transmitted from asecond antenna during the first time slot, and the second block to betransmitted from the second antenna during the second time slot inresponse to instructions from the processor.
 7. A method of generatingsymbols for transmission comprising: generating a first block comprisinga first sequence; generating a second block comprising a secondsequence; forming a reversed complex conjugate of the first block;forming a reversed complex conjugate of the second block; providing thereversed complex conjugate of the second block followed by the firstblock for transmission from a first antenna; and providing the reversedcomplex conjugate of the first block followed by the second block fortransmission from a second antenna.
 8. The method of claim 7, whereinthe first block consists of a first symbol and the second block consistsof a second symbol.
 9. The method of claim 8, wherein the first symboland the second symbol are consecutive symbols of a symbol stream. 10.The method of claim 7, wherein the first symbol and the second symbolare non-consecutive symbols of a symbol stream.
 11. A method ofgenerating blocks for transmission comprising: generating a first block;generating a second block; forming a complex conjugate of the secondblock, the complex conjugate of the second block is in a first order;and providing the complex conjugate of the second block in an inverse ofthe first order followed by the first block for transmission from afirst antenna.
 12. The method of claim 11, wherein the wherein the firstblock consists of a first symbol and the second block consists of asecond symbol.
 13. The method of claim 12, wherein the first symbol andthe second symbol are consecutive symbols of a symbol stream.
 14. Themethod of claim 12, wherein the first symbol and the second symbol arenon-consecutive symbols of a symbol stream.
 15. The method of claim 11,further comprising forming a reversed complex conjugate of the firstblock and providing the complex conjugate of the first block followed bythe second block for transmission from a second antenna.
 16. The methodof claim 15, further comprising generating a third block, forming areversed complex conjugate of the third block, wherein providing thecomplex conjugate of the first block followed by the second block fortransmission from a second antenna comprises providing the complexconjugate of the first block followed by the complex conjugate of thethird block followed by second block for transmission from a secondantenna.
 17. A transmitter comprising: at least two antennas; at leastone IFFT block comprising an input and an output; and an encodercomprising an input coupled to the output of the at least one IFFT blockand an output that provides a first symbol pair to be transmitted from afirst antenna and a second symbol pair to be transmitted from a secondantenna, wherein the first symbol pair comprises a first symbolcomprising a first sequence and a second symbol pair comprising a secondsequence and the second symbol pair comprises a complex conjugate of thesecond symbol in an inverse order of the second sequence and a complexconjugate of the first symbol in an inverse order of the first sequence.18. The transmitter of claim 17, wherein the first time slot and thesecond time slot are consecutive time slots.
 19. The transmitter ofclaim 17, wherein the first symbol and the second symbol are consecutivesymbols of a symbol stream.
 20. The transmitter of claim 17, wherein thefirst symbol and the second symbol are non-consecutive symbols of asymbol stream.
 21. A receiver comprising: a receive antenna adapted toreceive sequences; and a processor configured to generate complexconjugates of sequences received during a first time slot, to processsequences received during a second time slot following the first timeslot without generating complex conjugates, and to combine the complexconjugates of sequences received during the first time slot and thesequences received during the second time slot to generate decodedsymbols.
 22. The receiver of claim 20, wherein the first time slot andthe second time slot are consecutive time slots.
 23. The receiver ofclaim 20, the sequences comprise symbols and wherein the processor isfurther configured to reverse an order of at least some of the complexconjugates of the sequences.
 24. The receiver of claim 20, wherein afirst received sequence and a second received sequence are representedby vectors Y_(i) and Y_(i+1) where $\begin{bmatrix}Y_{i} \\{\overset{\_}{Y}}_{i + 1}\end{bmatrix} = {{\begin{bmatrix}\Lambda_{1} & {- \Lambda_{2}} \\\Lambda_{2}^{*} & \Lambda_{1}^{*}\end{bmatrix}\begin{bmatrix}{\hat{X}}_{i} \\{\overset{\hat{\_}}{X}}_{i + 1}\end{bmatrix}} + \begin{bmatrix}V_{i} \\{\overset{\_}{V}}_{i + 1}\end{bmatrix}}$ wherein Λ₁ is the impulse response associated with thefirst transmit channel, wherein Λ₂ is the impulse response associatedwith second transmit channel, wherein Λ₁* and Λ₂* respectively representcomplex conjugates of Λ₁, Λ₂, and wherein $\begin{bmatrix}V_{i} \\{\overset{\_}{V}}_{i + 1}\end{bmatrix}$ represents noise associated with first and secondtransmit channels, wherein {circumflex over (X)}_(i) corresponds to anestimate of X_(i), and wherein {overscore ({circumflex over (X)})}i+,corresponds to an estimate of X_(i+1).
 25. The receiver of claim 23,wherein the processor is further configured to generate vectors Z_(i),and Z_(i+1) from Y_(i) and {overscore (Y)}_(i+1), defined by:$\begin{bmatrix}Z_{i} \\Z_{i + 1}\end{bmatrix}\bullet{{\overset{\sim}{D}}^{- 1} \cdot \begin{bmatrix}{{\Lambda_{1}^{*}Y_{i}} + {\Lambda_{2}{\overset{\_}{Y}}_{i + 1}}} \\{{{- \Lambda_{2}^{*}}Y_{i}} + {\Lambda_{1}{\overset{\_}{Y}}_{i + 1}}}\end{bmatrix}}$ wherein ${\overset{\sim}{D} = {D + {\frac{1}{\rho}I}}},$wherein I is an identity matrix, wherein D Λ₁Λ₁*+Λ₂Λ₂*, and wherein ρrepresents a signal-to-noise ratio.
 26. A transmitter comprising: atleast three antennas; and a processor that causes generation of reversedcomplex conjugates of a plurality of blocks utilizing an inverse fastFourier transform, and that causes the plurality of blocks and reversedcomplex conjugates of the plurality of blocks to be transmitted from theat least three antennas in a plurality of consecutive time slotsaccording to a transmission scheme based upon a unitary matrix.
 27. Thetransmitter of claim 26, wherein the plurality of blocks comprises aplurality of time domain symbols.
 28. The transmitter of claim 27,wherein the plurality of time domain symbols are consecutive symbols ofa symbol stream.
 29. The transmitter of claim 27, wherein the pluralityof time domain symbols are non-consecutive symbols of a symbol stream.30. The transmitter of claim 26, further comprising a memory that storesthe plurality of blocks and reversed complex conjugates of the pluralityof blocks and that outputs the plurality of blocks and reversed complexconjugates of the plurality of blocks to be transmitted in the pluralityof consecutive time slots based upon the unitary matrix.
 31. A method ofgenerating symbols for transmission comprising: generating a pluralityof blocks; generating reversed complex conjugates of the plurality ofblocks utilizing an inverse fast Fourier transform; and providing theplurality of blocks and reversed complex conjugates of the plurality ofblocks to be transmitted from at least three antennas in a plurality ofconsecutive time slots according to a transmission scheme based upon aunitary matrix.
 32. The method of claim 31, wherein the plurality ofblocks comprises a plurality of time domain symbols.
 33. The method ofclaim 31, wherein the plurality of time domain symbols are consecutivesymbols of a symbol stream.
 34. The method of claim 31, wherein theplurality of time domain symbols are non-consecutive symbols of a symbolstream.